Residual-Space Evolutionary Optimization via Flow-based Generative Models

Zhuo Cao, Lena Krieger, Fernanda Nader, Xuan Zhao, Hanno Scharr, Ira Assent

Keywords: data optimization, conditional flow matching, counterfactual explanations, evolutionary algorithms

TL;DR: We propose residual-space evolutionary optimization, which combines flow-based generative editing with evolutionary search to support both local refinement and global exploration, with validation on MorphoMNIST and crystal data.

Abstract:

Data editing with generative methods typically requires differentiable objectives and gradient-based search. However, these assumptions break down in flow-based settings, where edits are performed through forward and backward integration and often involve non-differentiable or black-box objectives.
We introduce **residual-space evolutionary optimization**, a model-agnostic framework that addresses this gap by combining flow-based generative editing with evolutionary algorithms.
Building on the observation that conditional flow matching (CFM) can disentangle condition-controlled factors from instance-specific residuals, our framework directly operates in residual space and separates two complementary search regimes: **Self-pollination** performs local exploitation through feature-preserving residual refinement. **Cross-pollination** promotes broader exploration by recombining residuals across heterogeneous samples.
As a proof of concept, we validate the framework on **MorphoMNIST**, a benchmark dataset for counterfactual generation, and on **crystal data**. The results demonstrate that this exploration--exploitation decomposition provides a useful mechanism for balancing target alignment, instance preservation, and diversity, while extending beyond images to real-world scientific domains.

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Submission Number: 141